Novel cake-cutting and envy-free share notions for divisible goods are simultaneously achievable only up to a tight Θ(√n) approximation in the worst case.
On best-of-both-worlds fair-share allocations
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Fair Division via the Cake-Cutting Share
Novel cake-cutting and envy-free share notions for divisible goods are simultaneously achievable only up to a tight Θ(√n) approximation in the worst case.